To unlock the A Brother's Seduction trophy in Assassin's Creed Odyssey, you need to have Update 1.1.3 installed and have completed at least Chapter 5 of the main quest.
The first quest of this arc, Prodigal Son's Return, can be found at the Alter of the Cyclops in the Isthmus of Poseidon region of Korinthia. The closest viewpoint is the Temple of Apollo in Korinth. The quest will be highlighted on the map with a blue diamond with an exclamation mark in the middle.
Prodigal Son's Return
Once you arrive at the Alter of the Cyclops, defeat the bandits in the area and pick up Lykinos from the floor and escort him to his father's house at the Port of Kechries in Kraneion Plains. Once you place Lykinos on the floor go through the dialogue to complete the quest. Once completed you will have two new quests available.
You will have to find and kill a group of bandits located in the Ruined Temple of Zeus, which can be found to the west in the Kraneion Plains. Once the last bandit is killed, the quest is completed.
Dressing up for Charon
Timotheos will require you to recover Diokles' Athenian Armour from a merchant located in the Grove Kromyon area Korinthia. Talk to the merchant and he will give you a choice of buying the armour for 7,500, a cheaper version for 250, both for 7,750 or you can fight him for it. You will be able to unlock the trophy regardless of which choice you make. Once you have acquired the armour, the quest will be completed.
Honoring the Dead
Travel to the cemetery on the outskirts of Kraneion Plains and talk to Timotheos. Follow the dialogue and you will be asked to help gather the offering of wine and oil for the funeral from Sea Captain Dock which is located to the east. Once you have collected the items, return to Lykinos and Timotheos at the cemetery. Talk to them and you will have another choice to make. As previously, you will still unlock the trophy regardless of which one you choose. After some more dialogue, you can choose to give one or both of the offerings to the brothers.
Talk to Lykinos in his house at the Port of Kechries. Go through the dialogue and you will be asked to gather 2 x deer meat. Travel to the southern forests of Isthmus of Poseidon located just north. Once you have killed the deer and looted the meat, return to Lykinos located on top of a hill to the south of the Kreneion Plains and talk to him. Once the dialogue choices have been exhausted, you will complete the quest.
Wounds of Days Gone By
Talk to Timotheos who is located on a small island to the east of Kraneion Plains near the Isle of Salamis. Defeat him in the sparring match and then follow the dialogue making whichever of the choices you wish.
Return to the brothers' house at the Port of Kechries and talk to Lykinos. Travel to the Palace of Agamemnon in Argolis. Find and free Timotheos from the bandits. Once freed, kill the remainder of the bandits. Once the dialogue is complete, kill Hypatos and his men.
Once the Moving On quest is completed, you will unlock the A Brother's Seduction trophy.